Year: 2016
Author: Jerry L. Bona, Min Chen
Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 205–220
Abstract
Studied here is the Boussinesq system $$η_t+u_x+(ηu)_x+au_{xxx}-bη_{xxt}=0,$$ $$u_t+η_x+\frac{1}{2}(u²)_x+cη_{xxx}-du_{xxt}=0,$$of partial differential equations. This system has been used in theory and practice as a
model for small-amplitude, long-crested water waves. The issue addressed is whether
or not the initial-value problem for this system of equations is globally well posed.
The investigation proceeds by way of numerical simulations using a computer code
based on a a semi-implicit, pseudo-spectral code. It turns out that larger amplitudes
or velocities do seem to lead to singularity formation in finite time, indicating that the
problem is not globally well posed.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v49n3.16.01
Journal of Mathematical Study, Vol. 49 (2016), Iss. 3 : pp. 205–220
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Boussinesq systems global well-posedness singular solutions Fourier spectral method nonlinear water wave.